TY - JOUR
T1 - Crank-Nicolson ADI Finite Difference Method for Three-Dimensional Nonlinear Partial Integro-Differential Equations with Weak Singular Kernels
AU - Chen , Yanping
AU - Wang , Ruru
AU - Qiao , Leijie
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 867
EP - 889
PY - 2025
DA - 2025/06
SN - 15
DO - http://doi.org/10.4208/eajam.2024-088.301024
UR - https://global-sci.org/intro/article_detail/eajam/24200.html
KW - Three-dimensional nonlinear integral differential equation, alternating direction implicit method, finite difference method, stability, convergence.
AB - <p style="text-align: justify;">The main objective of this study is to present a fast and efficient numerical
scheme for solving nonlinear integral differential equations with weak singular kernels in
three-dimensional domain. First, the temporal derivative and integral term are approximated by the Crank-Nicolson (CN) method and the second-order fractional quadrature
rule. After that the spatial discretization is carried out by combining the finite difference method and the alternating direction implicit (ADI) method, and the nonlinear
term are approximated using the Taylor expansion. The stability and convergence of
the proposed scheme are analyzed, followed by the verification of the theoretical results
through numerical experiments.</p>